Servo DC Motor Position Control Based on Sliding Mode Approach Ahmed. M. Kassem* and Ali M. Yousef** * Control Technology Dep., Bini-Swief University, Egypt ** Electrical Dept., Assiut University, Egypt Abstrac - A novel controller based on the sliding mode models the desired closed loop performance. Secondly, (SM) approach is designed for controlling DC motor in a control law is designed such that the system state a servo drive. The modeling and analysis of the servo trajectory is forced toward the sliding surface. The DC motor are obtained. The sliding mode controller system state trajectory in the period of time before (SMC) design changes such that its performance is reaching the sliding surface is called the reaching substantially improved. To improve the controller phase. The system dynamics in the reaching phase is performance in steady stat (zero error) the integral still influenced by uncertainties. Ideally, the switching sliding mode controller (ISMC) is used. Since the main of the control should occur at infinitely high frequency drawback of SMC is a phenomenon, the so-called to eliminate the deviation from sliding manifold. In chattering and resulting from discontinuous practice, the switching frequency is not infinitely high controllers. An ISMC with switched gains is used for due to the finite switching time. Thus, undesirable chattering reduction and controller robustness. For chattering appears in the control effort. Chattering is comparison, the proposed ISM with switched gains is highly undesirable because it excites unmodeled high compared with that of a PID controller. Digital frequency plant dynamics and this can cause simulations have been carried out in order to validate unforeseen instability [9]. Different studies tried to the effectiveness of the proposed scheme. The proposed solve this problem by combining fuzzy or neural controller offers very good tracking; it is highly robust, controller with the sliding mode [10,11]. reaches the final position very fast. Furthermore the application of the SM ensures reduction of the system In this paper, the position control of the DC motor order by one. Also, quick recovery from matched in servo drive has been developed based on SM disturbance in addition to good tracking ability is approach. A novel scheme using Integral sliding mode evaluated. Moreover, this scheme is robust against the (ISM) controller with switched gains has been parameters variations and eliminates the influence of investigated. The system responses are compared when modeling. PID controller is applied to the system. A PID controller is selected because the cost of Keywords : Servo DC motor, integral sliding mode implementation is inexpensive and is widely used in control, PID controller. industry. SMC methods yield nonlinear controllers which are robust against unmodeled dynamics and, 1. Introduction internal and external perturbations. Computer AC and DC servomotors [1-3] are in use in many simulations are performed to show the validity of the applications. Particularly, DC ones are used in proposed system. The results obtained with ISMC with computer peripherals and robot manipulators and are changed gains are compared with the traditional SMC characterized by: ability to produce full continuous and PID controller. The advantages and limitations of torque, controlled braking is relatively simple and low each method are discussed. cost as compared with similar AC drives at high powers. Sliding mode control theory was introduced 2. Plant Description for the first time in the context of the variable structure systems (VSS). It has become so popular that now it The plant consists of a DC motor with an inertial represents this class of control systems. Even though, load. The DC motor is separately excited and armature in its early stages of development, the SMC theory was controlled, which schematic diagram is shown in Fig.1. overlooked because of the development in the famous In this section we proposed to design a controller to linear control theory. Recently, the variable structure control the motor-load angle speed. The system control strategy using the sliding-mode has been parameters are shown in appendix. A block diagram of focused on many studies and research for the control of the DC servomotor with automatic voltage regulator the DC servo drive systems [4-8]. The sliding-mode (AVR) is shown in Fig.2. control can offer many good properties, such as good performance against unmodeled dynamics, insensitivity to parameter variations, external disturbance rejection and fast dynamic response [9]. These advantages of the sliding-mode control may be employed in the position and speed control of an DC servo system. The design of SMC consists of two main steps. Firstly; one can select a sliding surface that Fig.1: DC Servomotor circuit diagram ˺ The state equations that describe the DC servomotor C a positive constant behavior [12] are: From the second theorem of Lyapunov, the stability condition can be written as: 2 2 d K m K f d 1 d ia TL (1) K (8) dt 2 J J dt 2 dt dia Ra K b d Va 1 2 ia (2) Where: 0 (positive definite) is a Lyapunov dt La La dt La 2 function and K a positive constant. The control voltage Let command is calculated by substituting and in equation (8) as follows [13]: Va u (3) 2 Substituting (1) into (2) and using (3) one gets: BRa Km r C r C 2 2 R J R J K d BR K d 1 u a m a m (9) u m a m T (4) 2 L Km 1 Ra J m dt Ra J m dt J m T K sign( ) J L In state space matrix form, one gets: m A block diagram of this conventional SM controller is dx A x B u D v (5) shown in Fig.3. dt Where 0 1 0 2 A BR K , B K m , 0 a m Ra J m Ra J m 0 1 D (6) J m t d with x x x , x , x , v T Fig. 3: Block diagram of the conventional SM 1 2 1 2 dt L controller and The problem with this conventional controller is x1 rotor position, that it has large chattering in the control output and the x rotor speed 2 drive is very noisy. Furthermore, because of chattering, u control input it is difficult to achieve small enough positioning error v disturbance in steady state [13]. To reduce chattering the sign t transpose function (infinite gain) of the conventional SM is substituted with a finite gain K within a small boundary. This affects controller's robustness too, but still the controller will remain robust enough if gain K is chosen large enough. An infinite or very large gain K increases chattering because the bandwidth of the automatic voltage regulator (AVR) is not infinite. We assumed an ideal AVR and did not include it in the plant model, but this assumption holds as long as the bandwidth of the outer control loops does not exceed Fig. 2: Block diagram of the DC motor with AVR. that of AVR. The selection of a finite K gain affects the sliding surface. By choosing a finite, appropriate value for K the chattering is greatly reduced [13]. The constant C basically determines the speed of response. 3. The Integral Sliding Mode (ISM) Controller It is the only parameter, which determines the dynamic of the system in SM. The choice of the constant C is In this section we will show first the design of also bounded from the AVR bandwidth and the the SM controller and later, based on the analysis and encoder noise. Large values of constant C tend to faster interpretation of the controller block diagram we response, but if the bandwidth of the AVR is exceeded introduce the proposed ISM controller. this will lead in chattering and it will deteriorate the The sliding surface is defined as: controller performance. e C e r C r (7) Where To reduce greatly the steady state error an integral block is added, which forces the system in steady state r the position reference ˻ toward a zero error positioning. This integral block 1 K(s) K (1 T s) (10) tends to slow down the transient response of the p T s D control system. For this reason it is switched on only I when the system approaches the final position. On one K P where K p , and K P TD represent the hand the sliding mode tracks the reference very fast TI ensuring a very small tracking error till the final proportional, integral and derivative gains of the positioning is reached and on the other hand the controller respectively. Define integral block, taking advantage of the small initial 1 1 T error, reduces it to zero very fast. The gain K is and I as the controller's n 2 T switched to a larger value K1 right before the position TI TD D command reaches the desired final value. The natural frequency and the damping coefficient, condition of switching is detected when speed and respectively. Then the PID transfer function can be acceleration signals of the position command have written as: opposite signs. This gain is returned to its previous 2 2 value immediately after the final position is reached. n 2 n s s K(s) K P (11) This ensures a fast and precise stop of the servo. If a 2 n s large gain will be applied all the time, chattering in the torque command will be inevitable. So, we have 5. Results and discussion designed a controller, which has a very good tracking and reaches very fast the final position. The controller The purpose of this part showing the validity and is also very robust to the outside disturbances or robustness of the proposed SMC approaches as applied parameter uncertainties.